Two-pump optical parametric devices having reduced stimulated Raman scattering noise levels

ABSTRACT

Two-pump optical parametric devices (OPDs), and methods of operating the same, generate desired output signals and idlers having reduced stimulated Raman scattering (SRS) noise levels. When the two-pump OPD is used as a two-pump optical parametric amplifier (OPA), the pumps are polarized perpendicular to each other, and the lower-frequency sideband (signal or idler) is polarized parallel to the lower-frequency pump (perpendicular to the higher-frequency pump). The desired output may be an amplified signal or a generated idler. When the two-pump OPD is used as a two-pump optical frequency converter (OFC), the pumps can be polarized parallel to one another, in which case the signal and idler are both perpendicular to the pumps, or perpendicular to one another, in which case the lower-frequency sideband (signal or idler) is polarized parallel to the lower-frequency pump (perpendicular to the higher-frequency pump).

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to a continuation-in-part (CIP) U.S. patentapplication Ser. No. 11/068,555, filed Feb. 28, 2005, the teachings ofwhich are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to optical parametric devices (OPDs), suchas optical parametric amplifiers (OPAs) and optical frequency converters(OFCs), and more particularly to two-pump OPDs having reduced stimulatedRaman scattering (SRS) noise levels in their output signals or idlers.

BACKGROUND OF THE INVENTION

Optical communication systems employ optical amplifiers, e.g., tocompensate for signal attenuation in optical fibers. One type ofamplifier that may be used in a fiber-based communication system is anOPA. As known in the art, an OPA is a device that produces a tunablecoherent optical output via a nonlinear optical processes calledfour-wave mixing (FWM), in which two photons from one pump wave, or twopump waves, are destroyed and two new photons are created, withconservation of the total photon energy and momentum. The wavescorresponding to the two new photons are usually referred to as thesignal wave and the idler wave. This process amplifies a weak inputsignal and generates an idler, which is a frequency converted (FC) andphase-conjugated (PC) image of the signal. As known in the art, there isanother type of FWM process, in which one signal photon and one pumpphoton are destroyed, and one idler photon and one different pump photonare produced, with conservation of the total photon energy and momentum.This process transfers power from the signal to the idler, which is a FCimage of the signal. Optical frequency converters, OFCs, can be used toperform switching and routing in communication systems. The fundamentalsof FWM are discussed in a book by G. P. Agrawal [“Nonlinear FiberOptics, 3rd Edition,” Academic Press, 2001, hereafter referred to asGPA].

However, a problem with two-pump OPDs is the SRS noise that appears inthe output signals and idlers. Because of SRS noise, the output signalsor idlers produced by OPDs have lower signal-to-noise ratios (SNRs) thanthe input signals, which reduces the effectiveness of OPDs incommunication systems.

SUMMARY OF THE INVENTION

In accordance with the present invention, two-pump OPDs, and methods ofoperating the same are described, which generate desired output signalsand idlers having reduced SRS noise levels. In the case of a two-pumpOPA, the pumps are polarized perpendicular to each other, and thelower-frequency sideband (signal or idler) is polarized parallel to thelower-frequency pump (perpendicular to the higher-frequency pump). Thedesired output may be an amplified signal or a generated idler(frequency-shifted copy of the signal). In the case of a two-pump OFC,the pumps can be polarized parallel to one another, in which case thesignal and idler are both perpendicular to the pumps, or perpendicularto one another, in which case the lower-frequency sideband (signal oridler) is polarized parallel to the lower-frequency pump (perpendicularto the higher-frequency pump). The desired output may be an amplifiedsignal or a generated idler.

More particularly, I describe a method of operating a two-pump opticalparametric device, OPD, as an amplifier, OPA, that generates a desiredoutput signal having a reduced stimulated Raman scattering, SRS, noiselevel. The method comprising the steps of

-   -   (1) applying first and second polarized pumps to the OPA, the        frequency of the first pump, P₁, being lower than the frequency        of the second pump, P₂, and the polarization of P₁ being        perpendicular to the polarization of P₂;    -   (2) applying a polarized input signal S as an inner sideband        adjacent to P₁ or P₂;    -   (3) outputting the desired output signal from an inner sideband        adjacent to P₁ or P₂;    -   (4) wherein the inner sideband adjacent to P₁ is polarized        parallel to P₁ and wherein        -   (a) when the desired output is an amplified signal S, the            input signal S is applied as an inner sideband adjacent to            P₁ and the SRS noise level in the desired output signal is            reduced by establishing the polarization of S to be            perpendicular to the polarization P₂ and        -   (b) when the desired signal is a generated PC idler, 2−, the            input signal S is applied as an inner sideband adjacent to            P₂ and the SRS noise level in idler 2− is reduced by            establishing the polarization of S to be parallel to the            polarization of P₂.

According to one embodiment, I describe a two-pump optical parametricamplifier, OPA, to generate a desired output signal having a reducedstimulated Raman scattering, SRS, noise level. The OPA comprises

-   -   a first polarized coupler for coupling a first pump, P₁, to the        two-pump OPA;    -   a second polarized coupler for coupling a second pump, P₂, to        the two-pump OPA, wherein the frequency of P₁ is lower than the        frequency of P₂ and the polarization of the first polarized        coupler is perpendicular to the polarization of the second        polarized coupler;    -   a third polarized coupler for coupling an input signal S in an        inner sideband adjacent P₁ or P₂;    -   means for outputting the desired output signal (or idler) from        an inner sideband adjacent to P₁ or P₂, and    -   wherein the inner sideband adjacent to P₁ is polarized parallel        to P₁ and wherein        -   (a) when the desired output is an amplified signal S, the            input signal S is applied as an inner sideband adjacent to            P₁ and the SRS noise level in the desired output signal is            reduced by establishing the polarization of S to be            perpendicular to the polarization P₂ and        -   (b) when the desired signal is a generated PC idler, 2−, the            input signal S is applied as an inner sideband adjacent to            P₂ and the SRS noise level in the idler 2− is reduced by            establishing the polarization of S to be parallel to the            polarization of P₂.

According to another aspect of the invention, I describe a method ofoperating a two-pump optical parametric device, OPD, as an opticalfrequency converter, OFC, to convert an input signal at a firstfrequency to a desired output idler I at a second frequency having areduced stimulated Raman scattering, SRS, noise level. The methodcomprising the steps of:

-   -   (1) applying a first polarized pump, P₁, and a second polarized        pump, P₂, to the OFC, the frequency of P₁ being lower than the        frequency of P₂;    -   (2) applying a polarized input signal S as an inner sideband 1+        adjacent to P₁ or an outer sideband 2+ adjacent to P₂; and    -   (3) outputting the desired output idler I from an outer sideband        2+ adjacent to P₂ or an inner sideband 1+ adjacent to P₁.

In another embodiment, I describe a two-pump optical frequencyconverter, OFC, for converting an input signal at a first frequency to adesired output idler at a second frequency having a reduced stimulatedRaman scattering, SRS, noise level. The OFC comprises

-   -   a first polarized coupler for coupling a first pump, P₁, to the        two-pump OFC;    -   a second polarized coupler for coupling a second pump, P₂, to        the two-pump OFC, wherein the frequency of P₁ is lower than the        frequency of P₂;    -   a third polarized coupler for coupling an input signal S in an        inner sideband 1+ adjacent to P₁ or an outer sideband 2+        adjacent to P₂; and    -   means for outputting the desired output idler, I, from an outer        sideband 2+ adjacent to P₂ or an inner sideband 1+ adjacent to        P₁.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and advantages of the present invention willbecome more fully apparent from the following detailed description, theappended claims, and the accompanying drawings in which:

FIG. 1 shows a two-pump OPD in accordance with one embodiment of thepresent invention;

FIG. 2 illustrates a representative frequency structure in the OPD ofFIG. 1;

FIG. 3 shows the spectral (frequency) characteristics of an input signal(S) that is simultaneously amplified and replicated within four outputspectral bands. If the signal is in band 1+, the 1−, 2− and 2+ bands arereferred to as idler (I) bands;

FIG. 4 shows an illustration of the SRS noise signals (SRS1 and SRS2)for a two pump OPA, where the two pumps P1 and P2, the input signal S inband 1+, and idler I in band 2− are all parallel polarized;

FIG. 5 shows the input signal S in band 2− and the idler I in band 1+,reversed from the positions shown in FIG. 4;

FIG. 6 shows the SRS2 noise when the polarization of the input signal Sin band 1+ is parallel to pump P2;

FIG. 7 shows the SRS2 noise when the polarization of the input signal Sin band 1+ is perpendicular to pump P2;

FIG. 8 shows the SRS2 noise when the polarization of the input signal Sin band 2− is parallel to pump P2;

FIG. 9 shows the SRS2 noise when the polarization of the input signal Sin band 2− is perpendicular to pump P2;

FIG. 10 shows the general frequency characteristics of the invented OPA,in which the desired output signal is in band 1+ (or 2−) and an idler isin band 2− (1+);

FIGS. 11A through 11C show the decrease in n₁₊ as the idler 1+ increasesin frequency from the frequency of pump P1 to the frequency of pump P2;

FIG. 12 shows that when the pumps P1 and P2 are parallel and idler 1+ isperpendicular to P1, then n₁₊ is zero and idler 2+ is perpendicular toP1;

FIG. 13 shows that when the pump P1 is perpendicular to pump P2 andidler 1+ is parallel to P1, then n₁₊ and R₂₊ are zero and idler 2+ isperpendicular to P1; and

FIG. 14 shows that when the pump P1 is perpendicular to pump P2 andidler 1+ is perpendicular to P1, then no idler 2+ is generated.

DETAILED DESCRIPTION

FIG. 1 shows, in accordance with one embodiment of the presentinvention, a two-pump OPD 100 that is configured for use in a long-haultransmission line of an optical communication system. OPA 100 is coupledbetween two sections 102 and 102′ of long-haul optical fiber. The inputoptical signal S from section 102 is received or coupled viapolarization coupler 103 to a coupler 104 of the OPA 100. The coupler104 is configured to combine an input signal S from section 102 with twodifferent pump waves generated by two pump-wave sources (e.g., lasers)111 and 112. The output of pump sources 111 and 112 are received orcoupled via polarization couplers 113 and 114, respectively, and arecombined in coupler 115. The combined two-pump signal P₁+P₂ from coupler115 is then further combined with input signal S in coupler 104.Depending on the implementation of OPD 100, each of the pump wavesources 111 and 112 may be a continuous-wave (CW) or pulsed opticalfield. The combined optical output from coupler 104 is coupled into ahighly nonlinear fiber (HNF) 108, in which the signal is amplified byFWM. Frequency shifted copies of the signal are also produced. While thepresent invention describes the use of HNF 108 for OPA and OFC, itshould be understood that other χ⁽³⁾ media that exhibit FWM, such asKerr media, could be used. Additionally, a three-way coupler may be usedto replace couplers 104 and 115 to combine the input signal S with thetwo pumps P₁ and P₂. A filter 109 is placed at the end of HNF 108 topass the desired output optical sideband 110 (amplified signal orgenerated idler) and block the undesired sidebands. For example, if thedesired output sideband 110 is an amplified version of input signal Sfrom fiber 102, then filter 109 passes that amplified signal S andfilters out the pump signals P₁ and P₂, and the one or more idlersgenerated in the HNF 108. Conversely, if the desired output sideband 110is one of the idlers, then filter 109 filters out the pump signals P₁and P₂, the amplified signal S from fiber 102, and the undesired idlersgenerated in the HNF 108. The desired output signal 110 is thentransmitted over section 102′. One attractive feature of a two-pump OPD100 is that the desired output sideband 110 can be selected to be anamplified or non-amplified, and conjugated or non-conjugated, version ofinput signal S at an arbitrary frequency (wavelength). In accordancewith the present invention, as will be discussed in more detail in laterparagraphs, the polarization of each of the couplers 103, 113, and 114,is selected to control the polarization of the input signal S, pump 111,and pump 112, respectively, so as to minimize SRS noise in the desiredoutput signal 110 of OPD 100.

FIG. 2 shows a simplified diagram of the output frequency structuredeveloped in HNLF 108 of OPD 100. In addition to two pumps labeled P₁and P₂ and located at frequencies ω₁ and ω₂, respectively, and a signalS (illustratively a sideband at frequency ω₁₊), various FWM processes inHNLF 408 produce three complementary sidebands at frequencies ω¹⁻, ω²⁻,and ω₂₊. In general, the frequency of the signal S may be at any one ofthe four sidebands, with the remaining three sidebands being generatedby FWM processes in OPD 100.

The following paragraphs describe the FWM processes in OPD 100 leadingto the frequency structure of FIG. 2. Suppose that the optical signal Sis at frequency ω₁₊ and the remaining three sidebands ω¹⁻, ω²⁻, and ω₂₊are idler sidebands. Then a modulation interaction (MI) produces thefirst idler sideband at frequency ω₁₊, according to thefrequency-matching condition2ω₁=ω¹⁻+ω₁₊,  (1)a phase-conjugated (PC) process produces a second idler sideband atfrequency ω²⁻ according to the frequency-matching conditionω₁+ω₂=ω₁₊+ω²⁻,  (2)and a Bragg scattering (BS), or frequency converter (FC), processproduces a third idler sideband at frequency ω₂₊ according to thefrequency-matching conditionω₁₊+ω₂=ω₁+ω₂₊.  (3)In addition, each of the three idler sidebands is coupled to the othertwo idler sidebands by an appropriate FWM process, i.e., MI, BS, or PC,which obeys an equation analogous to Eq. (1), (2) or (3).

In addition to the sidebands illustrated in FIG. 2, OPD 100 may alsogenerate several additional sidebands (not shown). For example, MI withP₂ generates additional sidebands with frequencies 2ω₂−ω¹⁻ and 2ω₂−ω₁₊and MI with P1 generates additional sidebands with frequencies 2ω₁−ω²⁻and 2ω₁−ω₂₊. However, unlike the four original sidebands shown in FIG.2, each of which is coupled to all of the other three, none of theadditional sidebands is coupled to all of the original four or all ofthe other three additional sidebands. Furthermore, for most values ofω₁₊, the additional sidebands are driven non-resonantly. Consequently,the effects of the additional sidebands on the operation of OPD 100 arenot considered further.

Since OPD 100 relies on FWM enabled by the Kerr effect to amplify andgenerate sidebands, the first and second pumps (P₁ and P₂) are notrequired to be applied to HNF 108 in a prescribed order; ω₁ and ω₂ arenot required to be derived based on or have a specific relationship withthe specific energy-level transitions of the material of the HNF 108;and neither pump power is required to exceed the level that produceselectromagnetically induced transparency (EIT) in HNF 108.

With reference to FIG. 3, there are shown illustrative frequencycharacteristics of a modulated input signal S, in band 1+, that issimultaneously amplified and replicated within four spectral bands 1−,1+, 2− and 2+. The generated idlers are either spectrally-mirroredimages of the modulated input signal S (idler bands 1− and 2−) or atranslated (frequency-shifted) replica (idler band 2+). Thespectrally-mirrored idlers are PCs, which offer the potential formitigating impairments. The four signal bands produced by two-pump OPD100 allow for considerable flexibility in selecting the properties ofthe desired output signal or idler. An inner band placement of inputsignal S (i.e., in bands 1+ and 2− located between the pumps P₁ and P₂)generates both an outer band nonPC (replica) and PCs located in theinner and outer bands. Thus, as shown in FIG. 3, an input signal S inband 1+ produces a nonPC in band 2+ and PCs in both inner band 2− andouter band 1−. An outer band placement of input signal S (i.e., in bands1− and 2+) generates both an inner band nonPC (replica) and PCs locatedin the inner and outer bands. The existence of multiple bands depends onthe presence of both pumps P₁ and P₂. The frequency of pumps P₁ and P₂can be tuned in ways such that the signals and idlers in all four bandsare strongly coupled, the signal and idler in bands 1+ and 2− arestrongly coupled (OPA enabled by PC), or the signal and idler in bands1+ and 2+ are strongly coupled (OFC enabled by BS).

Consider OPA enabled by phase-conjugated (PC) process. In this processγ₁+γ₂→γ₁₊+γ²⁻: Two pump photons (γ) are destroyed (one from each pump),and one signal and one idler photon are created. OPA is characterized bythe input-output relationsA ₁₊(z)=μ(z)A ₁₊(0)+ν(z)A ²⁻(0)*,  (4)A ²⁻(z)*=ν(z)*A ₁₊(0)+μ(z)*A ²⁻(0)*,  (5)where A₁₊ and A²⁻ are the amplitudes of the 1+ and 2− sidebands,respectively, and the transfer functions satisfy the auxiliary equation|μ|²−|ν|²=1 [C. J. McKinstrie, S. Radic and M. G. Raymer, “Quantum noiseproperties of parametric amplifiers driven by two pump waves,” Opt.Express 12, 5037-5066 (2004), hereafter referred to as MRR]. One canmodel the effects of SRS noise (approximately) by adding random (andindependent) amplitude fluctuations δa to each of the input amplitudes.Because ω₁₊ and ω²⁻ are both less than ω₂, δa₁₊ and δa²⁻ are bothnonzero (unless 1+ or 2− is perpendicular to P₂). If the input consistssolely of noise, the outputsR ₁₊(z)=|A ₁₊(z)|²=|μ(z)|² |δa ₁₊|²+|ν(z)|² |δa ²⁻|²=|μ(z)|² n₁₊+|ν(z)|² n ²⁻,  (6)R ²⁻(z)=|A ²⁻(z)|²=|ν(z)|² |δa ₁₊|²+|μ(z)|² |δa ²⁻|²=|ν(z)|² n₁₊+|μ(z)|² n ²⁻,  (7)where n₁₊ and n²⁻ are the input noise powers, and R₁₊ and R²⁻ are theoutput noise powers, respectively. The SRS noise photons at ω₊ areamplified by FWM, which also couples the noise photons at ω²⁻ to theoutput at ω₁₊. A similar statement can be made about the output at ω²⁻.These equations imply that R₁₊−R²⁻=n₁₊−n_(2−>)0 (unless 1+ isperpendicular to P₂). The gain G=|μ|². The auxiliary equation impliesthat |ν|²=G−1. In the high-gain regime (G>>1), |ν|²≈|μ|², andR₁₊≈R²⁻≈G(n₁₊+n²⁻). Thus, as a general rule, one can minimize the noisein both outputs by setting 1+ perpendicular to P₂, in which case n₁₊=0[R. H. Stolen, “Polarization effects in fiber Raman and Brillouinlasers,” IEEE J. Quantum. Electron. 15, 1157-1160 (1979), hereafterreferred to as RHS].

With reference to FIG. 4, there is shown an illustration of theresulting SRS noise fields SRS1 and SRS2 for a two-pump OPA 100, wherethe two pumps P₁ and P₂, input signal S (sideband 1+) and idler II(sideband 2−) are all parallel polarized. As shown, the SRS1 noise fieldlies in the same plane as the pump P₁ and the SRS2 noise field lies inthe same plane as the pump P₂. Since pumps P₁ and P₂ are parallel (i.e.,both are shown vertically polarized) SRS1 and SRS2 are in the sameplane. Note that the amplitudes of the SRS1 and SRS2 noise fieldsincrease to a well-defined peak values with increasing frequencyseparation from pumps P₁ and P₂, respectively. (For example, if thewavelength of pump P₂ is 1440 nm, then SRS2 peaks at about 110 nm fromthe pump wavelength, at about 1550 nm.) Notice that in the example ofFIG. 4, since the frequencies of the input signal S and idler I liebetween the frequencies of pumps P₁ and P₂, the SRS1 noise field has nodirect effect on these signals. Thus, since it is only the SRS2 noisefield that affects directly the desired output signal or idler 110 ofOPA 100, the effects of the SRS1 noise field will not be consideredfurther. It follows from Eqs. (6) and (7) that R₁₊=Gn₁₊+(G−1)n²⁻ andR²⁻=(G−1)n₁₊+Gn²⁻. Because noise photons at both input frequencies arecoupled to both outputs, the output noise powers of the sidebands arecomparable. However, R2− is slightly lower than R1+, as stated above. Inthis configuration, the idler is the desired output.

With reference to FIG. 5, there is shown the input signal S (in band 2−)and idler I (in band 1+) reversed from the positions shown in FIG. 4.Once again, it follows from Eqs. (6) and (7) that R₁₊=Gn₁₊+(G−1)n₂ andR²⁻=(G−1)n₁₊+Gn²⁻. Because noise photons at both input frequencies arecoupled to both outputs, the output noise powers of the sidebands arecomparable. However, R2− is slightly lower than R1+, as stated above. Inthis configuration, the signal is the desired output.

In accordance with the present invention, I have recognized that the SRSgrowth rate g_(R), and the amplified noise field that results, ispolarization dependent. As stated in [RHS], the SRS growth rate of asignal that is perpendicular to the pump is an order-of-magnitude lowerthat the growth rate of a signal that is parallel to the pump. Since theoutput amplitude A(z)=A(0)exp(g_(R)z), an order-of-magnitude differencein the gain exponent g_(R)z causes a many-orders-of magnitude differencein the gain exp(g_(R)z) and, hence, in the output amplitude A(z): Forpractical purposes, the SRS noise field that is perpendicular to pump 2can be neglected. Hence, in FIGS. 6-9 the noise field SRS2 is drawnparallel to pump 2.

In FIGS. 6-9 and the discussion that follows, two signals are said to beparallel if both signals are vertical or both signals are horizontal.Similarly, two signals are said to be perpendicular (orthogonal) if onesignal is vertical and the other is horizontal, or vice-versa. Theconcept of orthogonality is not limited to the linearly-polarized statesillustrated in the figures. For example, right-circularly-polarized andleft-circularly-polarized states are also orthogonal, even thoughneither state is linearly polarized [C. J. McKinstrie, H. Kogelnik, R.M. Jopson, S. Radic and A. V. Kanaev, “Four-wave mixing in fibers withrandom birefringence,” Opt. Express 12, 2033-2055 (2004), hereafterreferred to as MKJRK]. Although these figures were drawn forlinearly-polarized states (horizontal and vertical), they also representmore-general polarization states that are parallel or orthogonal. FIG. 6shows the input signal S in band 1+ polarized in direction X and theidler I in band 2− polarized in direction Y. FIG. 7 shows the inputsignal S in band 1+ polarized in direction Y and the idler I in band 2−polarized in direction X. FIG. 8 shows the input signal S in band 2−polarized in direction X and the idler I in band 1+ polarized indirection Y. FIG. 9 shows the input signal S in band 2− polarized indirection Y and the idler I in band 1+ polarized in direction X. InFIGS. 6-9 the polarization of the generated idler I is perpendicular tothe polarization of the input signal S [see reference MKJRK], regardlessof whether the idler frequency is higher or lower than the signalfrequency. In addition, the pumps P1 and P2 are perpendicular. (If pumpsP1 and P2 were parallel, a perpendicular input signal S would notgenerate an idler [MKJRK]. This configuration is not useful.) Theparametric gain produced by FWM is polarization-independent [MKJRK]: Itis the same regardless of whether the input signal S is parallel orperpendicular to pump P₁ (or P₂). For the configuration shown in FIG. 6,R₁₊=Gn₁₊ and R²⁻=(G−1)n₁₊. The output idler (2−) has slightly less noisethan the output signal (1+), but both are noisy. For the configurationshown in FIG. 7, R₁₊=(G−1)n²⁻ and R²⁻=Gn²⁻. The output signal (1+) hasslightly less noise than the output idler (2−), but neither is noisy. Ifthe desired output is the 1+ signal, the second configuration is better(because G−1<G and n²⁻<<n₁₊). If the desired output is the 2− idler, thesecond configuration is better (because G−1≈G and n²⁻<<n₁₊).

For the configuration shown in FIG. 8, R₁₊=(G−1)n²⁻ and R²⁻=Gn²⁻. Theoutput idler (1+) has slightly less noise than the output signal (2−),but neither is noisy. For the configuration shown in FIG. 9, R₁₊=Gn₁₊and R²⁻=(G−1)n₁₊. The output signal (2−) has slightly less noise thanthe output idler (1+), but both are noisy. If the desired output is the2− signal, the first configuration is better (because G−1≈G andn²⁻<<n₁₊). If the desired output is the 1+ idler, the firstconfiguration is better (because G−1<G and n²⁻<<n₁₊).

It follows from the analyses of FIGS. 6-9 that, if OPA 100 is to beoperated as a low-noise device, the higher-frequency sideband should beparallel to pump 2 (so the noise source is n2−). In this case thelower-frequency sideband has slightly less noise, but neither sidebandis noisy. This optimal configuration is illustrated in FIG. 10.

Now consider OFC enabled by BS. In this process γ₁₊+γ₂→γ₁+γ₂₊: One pumpand one signal photon are destroyed and one pump and one idler photonare created. OFC is characterized by the input-output relationsA ₁₊(z)=μ(z)A ₁₊(0)+ν(z)A ₂₊(0),  (8)A ₂₊(z)=−ν*(z)A ₁₊(0)+μ(z)*A ₂₊(0),  (9)where the transfer functions satisfy the auxiliary equation |μ|²+|ν|²=1[MRR]. As before, consider the effects of SRS noise, which are modeled(approximately) as random amplitude fluctuations δa added to the inputamplitudes. Because ω₂₊>ω₂, δa₂₊=0. It follows from this fact that, ifthe input consists solely of noise,R ₁₊(z)=|A ₁₊(z)|²=|μ(z)|² |δa ₁₊|²=|μ(z)|² n ₁₊,  (10)R ₂₊(z)=|A ₂₊(z)|²=|ν(z)|² |δa ₁₊|²=|ν(z)|² n ₁₊,  (11)where R₂₊ is the output SRS noise power at frequency ω₂₊.

First, suppose that 1+ is the signal and 2+ is the idler. Then theoutput noise R₂₊=|ν|²n₁₊. Because the 2+ idler is desired (A₂₊=−ν*A₁₊),in a typical experiment |ν|²≈1 and, hence, |μ|²≈0. If the pumps areparallel and 1+ is parallel to P₁, then R₂₊ is always nonzero. As ω₁₊increases from ω₁ to ω₂, n₁₊ decreases, as illustrated in FIG. 11. Ifthe pumps are parallel and 1+ is perpendicular to P₁, as illustrated inFIG. 12, then n₁₊=0, 2+ is generated perpendicular to P₁ [see MKJRK] andR₂₊=0: SRS noise is eliminated completely. If P₁ and P₂ areperpendicular and 1+ is parallel to P₁ (perpendicular to P₂), asillustrated in FIG. 13, then n₁₊=0, 2+ is generated perpendicular to P₁(parallel to P₂) [MKJRK] and R₂₊=0: SRS noise is eliminated completely.If P₁ and P₂ are perpendicular and 1+ is perpendicular to P₁ (parallelto P₂), as illustrated in FIG. 14, no 2+ idler is generated [MKJRK].

Second, suppose that 2+ is the signal and 1+ is the idler. Then theoutput noise R₁₊=|μ|²n₁₊. Because the 1+ idler is desired (A₁₊=νA₂₊), ina typical experiment |ν|²≈1 and, hence, |μ|²≈0: Most SRS noise photonsat ω₁₊ are frequency shifted to ω₂₊. Few remain at ω₁₊ to pollute theidler. SRS noise is eliminated completely if the pumps are parallel and2+ is perpendicular to P₂, in which case 1+ is generated perpendicularto P₂ [MKJRK], or if the pumps are perpendicular and 2+ is parallel toP₂ (perpendicular to P₁), in which case 1+ is parallel to P₁(perpendicular to P₂) [MKJRK]. If the pumps are perpendicular and 2+ isperpendicular to P₂ (parallel to P₁), no 1+ idler is generated [MKJRK].

It follows from the analyses of FIGS. 11-14 that, if OFC 100 is to beoperated as a low-noise device, the lower-frequency sideband should beperpendicular to pump 2 (so the noise source is zero). In this caseneither sideband has noise. These optimal configurations wereillustrated in FIGS. 12 and 13.

Various modifications of the described embodiments, as well as otherembodiments of the inventions (OPAs and OFCs), which are apparent topersons skilled in the art to which the inventions pertain, are deemedto lie within the principle and scope of the inventions as expressed inthe following claims.

Although the steps in the following method claims, if any, are recitedin a particular sequence with corresponding labeling, unless the claimrecitations otherwise imply a particular sequence for implementing someor all of those steps, those steps are not necessarily intended to belimited to being implemented in that particular sequence.

1. A two-pump optical parametric device, OPD, adapted to generate adesired output signal, comprising: an optical medium that exhibitsfour-wave mixing; one or more polarization couplers that apply a firstpolarized pump P₁, a second polarized pump P₂, and a polarized inputsignal S to the optical medium, wherein a frequency of the pump P₁ islower than a frequency of the pump P₂; and an optical filter thatselects an idler I or an amplified signal S as the desired outputsignal, wherein: the idler I is coupled to the pumps P₁ and P₂ and thesignal S via said four-wave mixing; and the one or more polarizationcouplers apply the pump P₁, the pump P₂, and the input signal S to theoptical medium so that, in a set of four optical signals consisting ofthe pumps P₁ and P₂, the signal S, and the idler I, two of the opticalsignals have a first polarization and the remaining two of the opticalsignals have a second polarization orthogonal to the first polarization.2. The two-pump OPD of claim 1, wherein: the polarization of the pump P₁is perpendicular to the polarization of the pump P₂; the input signal Sis configured as an inner sideband adjacent to a selected one of thepumps P₁ and P₂; the desired output signal is output from a respectiveinner sideband adjacent to the pump P₁ or the pump P₂, and the innersideband adjacent to the pump P₁ is polarized parallel to the pump P₁;if the desired output is the amplified signal S, then the input signal Sis configured as the inner sideband adjacent to the pump P₁ and thepolarization of the input signal S is configured to be perpendicular tothe polarization of the pump P₂ and if the desired signal is the idlerI, then the input signal S is configured as the inner sideband adjacentto the pump P₂ and the polarization of the input signal S is configuredto be parallel to the polarization of the pump P₂.
 3. The two-pump OPDof claim 2, wherein the frequencies of the pumps P₁ and P₂ are selectedto minimize outer-band idlers.
 4. The two-pump OPD of claim 2, whereinthe four-wave mixing is enabled by a phase-conjugating (PC) process. 5.The two-pump OPD of claim 1, wherein: the input signal S is configuredas an inner sideband adjacent to the pump P₁ or an outer sidebandadjacent to the pump P₂; if the input signal S is configured as theinner sideband adjacent to the pump P₁, then the OPD is configured tooutput the desired output signal from the outer sideband adjacent to thepump P₂; and if the input signal S is configured as the outer sidebandadjacent to the pump P₂, then the OPD is configured to output thedesired output signal from the inner sideband adjacent to the pump P₁.6. The two-pump OPD of claim 5, wherein: the polarizations of the pumpsP₁ and P₂ are parallel to each other; and the polarizations of thesignal S and the idler I are both perpendicular to the polarizations ofthe pumps P₁ and P₂.
 7. The two-pump OPD of claim 5, wherein: thepolarizations of the pumps P₁ and P₂ are perpendicular to each other;and the polarization of the inner sideband is parallel to thepolarization of the pump P₁.
 8. The two-pump OPD of claim 5, wherein thefrequencies of the pumps P₁ and P₂ are selected to minimize an outersideband adjacent to the pump P₁ and an inner sideband adjacent to thepump P₂.
 9. The two-pump OPD of claim 5, wherein the four-wave mixing isenabled by a Bragg scattering (BS) process.
 10. The two-pump OPD ofclaim 1, wherein the one or more polarization couplers comprise: a firstpolarization coupler that applies the polarized input signal S to theoptical medium; a second polarization coupler that applies the firstpolarized pump P₁ to the optical medium; and a third polarizationcoupler that applies the second polarized pump P₂ to the optical medium.